# Catching the "L" train

This is a more difficult version of an earlier puzzle.

Hit the "C" ball at such an angle that it creates a chain reaction which ultimately dislodges the "L" ball.

Whenever the ball in motion hits a stationary ball, the ball in motion replaces the stationary ball and forms a word. The stationary ball is then set in motion at an angle of your choosing.

Words formed after letter replacement should be common and well-known, not obscure or archaic. You may replace a letter with the same letter, if you wish.

You may use the bumper rails (a.k.a., cushions) to deflect the trajectory of the ball in motion. But don't worry too much about the exact angles of it.

I imagine this could be done with fewer moves, but here's how I got there...

...with a 23 ball combo shot and lots of fancy spin

Methodology:

I figured it in Excel so I could check my letter counts and then compared my table to the image. All exchanges are possible if I can hit enough walls, knock the object ball in a direction of my choosing (allowing all 360 degrees), and not worry too much about the exact angles. In the interest of brevity, I did not attempt to draw all the moves.

• It's looking good! Those are the same steps that I have. And you're right, with enough fancy spin and use of the walls, you can draw a continuous trajectory. BTW, according to my drawing, you don't need a full 360°. Just 180° is sufficient. (I.e., if the cue ball comes from the north, then the displaced ball exits the word to the south. If the cue ball comes from the south, then the displaced ball exits the word to the north.) Oct 25, 2022 at 14:22
• Does the answer require a visual solution like @cap provided on puzzling.stackexchange.com/questions/118415/release-the-q-ball? I honestly don't have the motivation to make that happen.
– will
Oct 25, 2022 at 17:35
• Your answer is sufficient and will earn the green checkmark. However, if you or someone else would like to provide a visual, that would be helpful in attracting interest and upvotes. Oct 25, 2022 at 17:47

For those interested in "the making of":

The shortest path to dislodging the "L" from ALOUD cannot be realized from the setup presented in this puzzle. The shortest path (at least according to my dictionary) comes from the setup ALOUD, FORK, BOT with initial strike ball "C". This allows the "L" to be dislodged in 19 steps.

See the 19 steps:

 0. ALOUD, FORK, BOT with "C" in motion
1. CLOUD, FORK, BOT with "A" in motion
2. CLOUD, FORK, BOA with "T" in motion
3. CLOUT, FORK, BOA with "D" in motion
4. CLOUT, DORK, BOA with "F" in motion
5. FLOUT, DORK, BOA with "C" in motion
6. FLOUT, DOCK, BOA with "R" in motion
7. FLOUR, DOCK, BOA with "T" in motion
8. FLOUR, DOCK, BOT with "A" in motion
9. FLOUR, DOCK, BAT with "O" in motion
10. FLOOR, DOCK, BAT with "U" in motion
11. FLOOR, DUCK, BAT with "O" in motion
12. FLOOR, DUCK, OAT with "B" in motion
13. FLOOR, BUCK, OAT with "D" in motion
14. FLOOD, BUCK, OAT with "R" in motion
15. FLOOD, BUCK, OAR with "T" in motion
16. FLOOD, TUCK, OAR with "B" in motion
17. BLOOD, TUCK, OAR with "F" in motion
18. BLOOD, TUCK, OAF with "R" in motion
19. BROOD, TUCK, OAF with "L" in motion

But I was uncomfortable with some of the slang-ish words in this sequence, so I decided to play it safe with ALOUD, FRET, BORN which requires a slightly longer path of 23 steps.

I am still not 100% happy with

FRAT

although its usage is becoming more common, according to Google Ngram Viewer.

BTW, what's my obsession with dislodging the "L" from ALOUD? Nothing, really. ALOUD doesn't even have the longest dislodging sequence. However, its dislodging sequence does have a very nice flavor, with a variety of words and uncommon letters.

The longest dislodging sequence (according to my dictionary) is dislodging the "N" from SMARTING which requires 14 steps.

See the 14 steps:

 0. SMARTING
1. STARTING
2. STARLING
3. STALLING
4. STALKING
5. STACKING
6. SLACKING
7. CLACKING
8. CLOCKING
9. CLOAKING
10. CROAKING
11. CREAKING
12. CREATING
13. CREATINE
14. CREATIVE

It feels a bit tedious and repetitive, so I went with ALOUD.

(No need to upvote any of this. Please upvote @will 's and @Seb 's marvelous answers.)

My solution starts like @will's, however I took one wrong step and ended up with a longer chain (and with a rude word towards the end, heads up):

27 steps:

ALOUD FRET BORN C
|
CLOUD FRET BORN A
|
CLOUD FRAT BORN E
|
CLOUD FEAT BORN R
|
CLOUD FEAR BORN T
|
CLOUT FEAR BORN D
|
CLOUT DEAR BORN F
|
FLOUT DEAR BORN C
|
FLOUT DEAR CORN B
|
FLOUT BEAR CORN D
|
|
|
FLOUR BEAT CORN D
|
FLOUR BEAT CORD N
|
FLOUR BENT CORD A
|
FLOUR BENT CARD O
|
FLOOR BENT CARD U
|
FLOOR BENT CURD A
|
FLOOR BEAT CURD N
|
FLOOR BEAN CURD T
|
FLOOR BEAN CURT D
|
FLOOD BEAN CURT R
|
FLOOD BEAR CURT N
|
FLOOD NEAR CURT B
|
BLOOD NEAR CURT F
|
BLOOD FEAR CURT N
|
BLOOD FEAR CUNT R
|
BROOD FEAR CUNT L


The way approached it was:

I tried to find a word ladder starting with ALOUD and ending with a word not spelled with L, while only using letters that are available in the three words. It was surprisingly constrained, which made me feel like I was on the right track. Once I was reasonably sure I needed to get to BLOOD -> BROOD, I involved the other words to swap the letters around.

Very enjoyable puzzle, took me much longer than the previous one in this style.

• Oh, wow! Nice job! And what a beautiful ASCII representation of the movement. Thank you for pointing out that it is surprisingly constrained. As you observed, I didn't just throw a random triplet of words together and start swapping letters. I first looked for words which had highly-constrained dislodge sequences. (In this case, dislodging the L from ALOUD can really only be done in one way.) And then, I built the triplet and their swapping sequence around that highly-constrained dislodge sequence. Nov 1, 2022 at 14:31
• BTW, you alluded to something very important that every programmer should note: If a programmer were to remove all the rude words prior to searching over the space, he might think he has found a long and challenging solution without realizing that there is a "rude word shortcut". He's in for a rude awakening when a solver points it out to him! The right way to do it is to run the algorithm once with the rude words excluded, and then again with the rude words included. Once to find, and once to verify. Anyway, thank you again for your solution, and I am impressed that you did it by hand! Nov 1, 2022 at 14:32